Senate Republican leaders moved Tuesday to include a repeal of the Affordable Care Act's individual mandate in their tax bill, a major change of strategy as they try to accomplish two of their top domestic priorities in a single piece of legislation.

They also announced that the individual tax cuts in the plan would be made temporary, expiring at the end of 2025 to comply with Senate rules limiting the impact of legislation on the long-term deficit. A corporate tax cut, reducing the rate from 35 to 20 percent, would be left permanent.

The changes introduce volatile variables into what was already a challenging political enterprise for Republicans. And it's unclear whether they will help or hurt the bill's chances.

Repealing the mandate, which compels most Americans to buy health insurance or pay a fine, would free up more than $300 billion in government funding over the next decade that Republicans could use to finance their proposed tax cuts, but it would result in 13 million fewer people having health insurance, according to projections from the nonpartisan Congressional Budget Office.

The CBO has also projected that repealing the individual mandate would drive up insurance premiums for many Americans by roughly 10 percent.

Eliminating the individual mandate and having far fewer people signed up for insurance saves money because many of those people receive federal subsidies to buy coverage. Senate leaders are using those savings to address the concerns of anxious members from across their caucus who complained that the tax plan's benefits for the middle class were too modest compared with benefits received by the wealthy and corporations.

Changes to the bill released Tuesday night by the Senate Finance Committee indicated that the savings would be used in part to allow individuals to claim a larger $2,000 child tax credit, a priority of Ivanka Trump, the president's daughter. They would also be used to modestly reduce income tax rates for middle-income taxpayers.

Senate Republicans also are seeking to deliver expanded benefits to "pass-through" firms that send profits to their owners to be taxed as individual income.

"We're optimistic that inserting the individual mandate repeal would be helpful," Senate Majority Leader Mitch McConnell (R-Ky.) said Tuesday after meeting with party members during a closed-door lunch.

At the same time, by making the individual income tax cuts temporary, Senate leaders are seeking to ensure that the bill does not violate the chamber's rules that prohibit legislation passed with fewer than 60 votes from raising the deficit after 10 years.

But while solving some problems, the changes Tuesday threaten new political problems of their own.

The attack on former president Barack Obama's signature legislative achievement is likely to rule out the already slim possibility of support from Democrats, and the prospect of adding millions to the ranks of the uninsured could trouble moderate Republicans who voted down previous repeal efforts.

Sen. Susan Collins (R-Maine), one of the Republicans who opposed earlier attempts to roll back the health-care law, said Tuesday that including the repeal measure "complicates" the tax effort. But she suggested she might be able to support it if the Senate also passes a bipartisan bill to preserve other aspects of the Affordable Care Act.

Sen. John McCain (R-Ariz.), who along with Collins and Sen. Lisa Murkowski (R-Alaska) voted down an Affordable Care Act repeal effort this summer, declined to say whether he would back a tax bill that included repeal.

"I want to look at the bill in its entirety before you start plucking out parts of it to see whether I support it or not," he said Tuesday in the Capitol.

Republicans control 52 votes of the 100-seat Senate, so the defection of three members would imperil any changes to the bill. Republicans are trying to pass the tax-cut bill through a process known as reconciliation, which requires only 50 votes — plus a tiebreaking vote from Vice President Pence — to pass the bill.

The Senate Finance Committee hopes to move a bill to the full Senate floor this week, with the entire chamber voting on it after Thanksgiving. The House plans to vote on its own version of the bill — which does not contain the individual mandate repeal or the sunsetting of the individual tax provisions — this week.

Senators concerned about restraining national debt — long one of the top goals for the GOP — may also raise howls about the plan to sunset the individual income tax cuts in 2025. Congress is unlikely to allow a large tax increase on taxpayers at that point, which could mean a big hit to the deficit over the long run.

Repealing the individual mandate would undermine the Affordable Care Act's system for attempting to get low-income people and other individuals into private health insurance plans. The health-care law banned insurance companies from discriminating against people with preexisting health conditions. But to prevent people from waiting to buy insurance until they got sick, the law also imposed financial penalties for individuals who did not maintain coverage.

A powerful group of stakeholders, including the major health insurance and hospital insurance lobbies and two influential doctors' groups, wrote a letter to leaders of both parties arguing that they should retain the individual mandate.

"There will be serious consequences if Congress simply repeals the mandate while leaving the insurance reforms in place: millions more will be uninsured or face higher premiums, challenging their ability to access the care they need," the groups wrote.

Broadly, both the Senate bill and House bill would sharply cut the corporate tax rate and cut income tax rates for individuals, while seeking to finance those cuts by eliminating or scaling back some popular tax deductions. What the deduction rollbacks don't cover would be financed by $1.5 trillion in deficit spending over a decade.

The House and Senate bills would lower taxes for many Americans, but nonpartisan analysts have concluded that the elimination of certain deductions would have millions pay higher taxes, particularly if they live in states such as New York, New Jersey or California.

The House and Senate must pass matching versions of the tax-cut bill for Trump to be able to sign them into law. The House bill does not include a repeal of the individual mandate.

House conservatives mounted a last-ditch effort Tuesday to include a repeal before the full chamber votes on the bill, scheduled for Thursday. Rep. Mark Walker (R-N.C.), the leader of the Republican Study Committee, huddled in the office of House Speaker Paul D. Ryan (R-Wis.) Tuesday afternoon with House Rules Committee Chairman Pete Sessions (R-Tex.), whose panel will make any final changes to the bill Tuesday night before it heads to the floor.

But House GOP aides who were not authorized to speak publicly on the internal discussions said GOP leaders are loath to make such a major change to the bill at this late stage and prefer to see whether the Senate could pass a bill with the repeal provision before bringing the issue up in the House.

In the Senate, the sudden shift in the tax bill threatens to undermine a compromise health measure negotiated between Sens. Patty Murray (D-Wash.) and Lamar Alexander (R-Tenn.). The agreement would resume payments that help low-income Americans afford health insurance, which the Trump administration halted in October.

To win support for the updated tax bill, the Senate could take up the Alexander-Murray bill alongside it, according to Sens. John Thune (R-S.D.) and Bob Corker (R-Tenn.). The bills cannot be combined under the rules of reconciliation.

Senate Minority Leader Charles E. Schumer (D-N.Y.) said including a repeal of the mandate in the tax bill would torpedo Democratic support for the Murray-Alexander compromise.

"We don't need to trade it for a tax bill, and we won't," he said.

And Murray, the top Democrat on the Senate Health, Education, Labor and Pensions Committee, told reporters she was stunned that Republicans would again seek to undo the Affordable Care Act.

"The elections last week clearly showed that the American people are paying attention, and they don't want their health care taken away," Murray said, referencing a string of state-level elections in Virginia, New Jersey and elsewhere in which Democrats trounced Republicans. "I don't think [Republicans are] listening."